Transition maps at non-resonant hyperbolic singularities are o-minimal Academic Article uri icon

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abstract

  • We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singularity p of X, a transition map for X at p is definable in this structure. This structure also defines all convergent generalized power series with natural support and is polynomially bounded.

publication date

  • January 2009